Homotopy solution to non-linear evolution for heavy nuclei

TL;DR

This paper introduces a homotopy method combining analytical and perturbative techniques to solve non-linear evolution equations for heavy nuclei, showing small non-linear corrections in the saturation region.

Contribution

The paper presents a novel homotopy approach that integrates analytical solutions and perturbative corrections for non-linear evolution equations in nuclear physics.

Findings

Non-linear corrections are small and manageable

Homotopy method effectively solves the evolution equation

Analytical solutions provide a solid starting point

Abstract

In the paper we suggest the homotopy method for solving of the non linear evolution equation. This method consists of two steps. First is the analytical solution for the linearized version of the non-linear evolution deep in the saturation region. Second, the perturbative procedure is suggested to take into account the remaining parts of the non-linear corrections. It turns out that these corrections are rather small and can be estimated in the regular iterative procedure.